Spontaneous Emission From Nonhermitian Perspective: Complex Scaling Of The Photon Coordinates

Spontaneous emission (SE) is usually studied within the framework of quantum dissipation theory. In this paper we pursue a different view of SE. Namely, we take advantage of Nonhermitian Quantum Mechanics (NHQM) and interpret SE as the decay of a Feshbach type resonance. Correspondingly, we aim at calculating the SE decay rate Gamma (resonance width) and the associated resonance wavefunction via the complex scaling (CS) method. Standard application of CS in NHQM is based on scaling the dissociative coordinates of the system, . In the case of SE, the decay consists in emitting photons. Therefore the CS must be applied on (suitably defined) position coordinates of the photons. Feasibility of such a programme is demonstrated explicitly through choosing the adequate photon coordinates and performing CS of the photon wavefunctions in the position representation. It is anticipated in this way that CS makes the full resonance wavefunction square integrable, and enables thus the calculation of Gamma by proceeding in complete analogy with the well established NHQM approaches. As an illustration, the standard Golden Rule formula for Gamma is rederived from the CS nonhermitian perturbation theory.